Question

if x= g and a = b then x+a = y+b write the euclid's axiom involved in the above statement

Answer 1

the euclid's axiom use here (since a is equal to b ) "if equals are added to equals the whole are equals

Answer 2

It is given here that

x=g .........(1)

a=b ..........(2)

adding (1) and (2), we get i.e L.H.S of (1) to L.H.S of (2) and R.H.S of (1) to R.H.S of (2), we get

→x+a= g+b

The Euclid Axiom used here is that if two equals are added with one another , the whole i.e combination of them are equal.

I am explaining it by giving an Example

Suppose l is a line,C and D are points on opposite side of point A. and there is a ray AB perpendicular to l.

So, ∠ CAB = 90°, ∠DA B= 90°

∵ ∠ CAB + ∠DAB = 90° +90°=180°

Which is the angle made by Semicircle or you call it Linear pair Axiom.

Which verifies that If two equals are added with one another , the combined of them are equal.